792 



SCIENCE 



[N. S. Vol. XXXVIII. No. 988 



Engineers tells us that engineering is the 

 ' ' art of directing the great sources of power 

 in Nature for the use and convenience of 

 man." By Nature here must be meant 

 external or physical nature, for, if internal 

 nature were also meant, every good form 

 of activity would be a species of engineer- 

 ing, and may be it is such, but that is a claim 

 which even engineers would hardly make 

 and poets would certainly deny. Use and 

 convenience — these are the key-bearing 

 words. It is perfectly evident that our 

 lecturer will have to deal first of all with 

 what the world would call the "utility" of 

 rigorous thinking, that is to say, with the 

 applications of mathematics and especially 

 with its applications to problems of engi- 

 neering. If he really knows profoundly 

 what mathematics is, he will not wish to 

 begin with applications or even to make ap- 

 plications a major theme of his discourse, 

 but he must, and he will do so uncomplain- 

 ingly as a concession to the external- 

 mindedness of his time and his audience. 

 He will not only desire to show his audi- 

 ence applications of mathematics to engi- 

 neering, but, being a historian of civiliza- 

 tion, he will especially desire to show them 

 the development of such applications from 

 the earliest times, from the building of 

 pyramids and the mensuration of land in 

 ancient Egypt down to such splendid 

 modern achievements as the designing and 

 construction of an Eads bridge, an ocean 

 Imperator or a Panama canal. The story 

 will be long and difficult, but it will edify. 

 The audience will be amazed at the truth 

 if they understand. If they do not under- 

 stand the truth fully, our speaker must at 

 all events contrive that they shall see it in 

 glimmers and gleams and, above all, that 

 they shall acquire a feeling for it. They 

 must be led to some acquaintance with the 

 great engineering works of the world, past 

 and present ; they must be given an intelli- 



gent conception of the immeasurable con- 

 tribution such works have made to the com- 

 fort, convenience and power of man; and 

 especially must they be convinced of the 

 fact that not only would the greatest of 

 such achievements have been, except for 

 mathematics, utterly impossible, but that 

 such of the lesser ones as could have been 

 wrought without mathematical help could 

 not have been thus accomplished without 

 wicked and pathetic waste both of material 

 resources and of human toil. In respect to 

 this latter point, the relation of mathe- 

 matics to practical economy in large affairs, 

 our speaker will no doubt invite his hear- 

 ers to read and reflect upon the ancient 

 work of Frontinus on the "Water Supply 

 of the City of Rome" in order that thus 

 they may gain a vivid idea of the fact that 

 the most practical people of historj^ despis- 

 ing mathematics and the finer intellectuali- 

 zations of the Greeks, were unable to accom- 

 plish their own great engineering feats 

 except through appalling waste of mate- 

 rials and men. Our lecturer will not be 

 content, however, with showing the service 

 of mathematics in the prevention of waste ; 

 he will show that it is indispensable to the 

 productivity and trade of the modern 

 world. Before quitting this division of his 

 subject he will have demonstrated that, if 

 all the contributions which mathematics 

 has made, and which nothing else could 

 make, to navigation, to the building of rail- 

 ways, to the construction of ships, to the 

 subjugation of wind and wave, electricity 

 and heat, and many other forms and mani- 

 festations of energy, he will have demon- 

 strated, I say, and the audience will finally 

 understand, that, if all these contributions 

 were suddenly withdrawn, the life and body 

 of industry and commerce would suddenly 

 collapse as by a paralytic stroke, the now 

 splendid outer tokens of material civiliza- 

 tion would perish, and the face of our 



